"Subjectivists should feel obligated to recognize that any opinion (so much more the initial one) is only vaguely acceptable [...] So it is important not only to know the exact answer for an exactly specified initial problem, but what happens changing in a reasonable neighborhood the assumed initial opinion." (Bruno de Finetti, "Prevision: Ses Lois Logiques, ses Sources Subjectives", Annales de l’Institute Henri Poincaré, 1937)
"An item of information which leads to the exclusion of
certain of the possible outcomes causes a decrease in entropy: this decrease is
called the amount of information, and, like the entropy, is measured in bits
(it is, in fact, the same thing with the opposite sign: some even call it
negative entropy)."
"Examples are always useful in order to give a sense of
concreteness to concepts introduced in a general and abstract form."
"From the theoretical, mathematical point of view, even the
fact that the evaluation of probability expresses somebody's opinion is then
irrelevant. It is purely a question of studying it and saying whether it is
coherent or not; i.e. whether it is free of, or affected by, intrinsic
contradictions. In the same way, in the logic of certainty one ascertains the
correctness of the deductions but not the accuracy of the factual data assumed
as premises."
"Given any set of events whatsoever, the conditions of
coherence impose no limits on the probabilities that an individual may assign,
except that they must not be in contradiction amongst themselves. [...] The conditions of coherence must exclude the possibility of
certain consequences whose unacceptability appears expressible and recognizable
to everyone, independently of any opinions or judgments they may have regarding
greater or lesser 'reasonableness' in the opinions of others."
"In reasoning, as in every other activity, it is, of course,
easy to fall into error. In order to reduce this risk, at least to some extent,
it is useful to support intuition with suitable superstructures: in this case,
the superstructure is logic (or, to be precise, the logic of certainty)."
"It is precisely in investigating the connection that must hold between evaluations of probability and decision-making under conditions of uncertainty that one can arrive at criteria for probabilities, for establishing the conditions which they must satisfy, and for understanding the way in which one can, and indeed one must, 'reason about them'. It turns out, in fact, that there exist simple (and, in the last analysis, obvious) conditions, which we term conditions of coherence: any transgression of these results in decisions whose consequences are manifestly undesirable (leading to certain loss)." (Bruno de Finetti, "Theory of Probability", 1974)
"Meanwhile, for those who are not aware of it, it is
necessary to mention that in the conception we follow and sustain here only
subjective probabilities exist - i.e. the degree of belief in the occurrence of
an event attributed by a given person at a given instant and with a given set
of in information. This is in contrast to other conceptions which limit
themselves to special types of cases in which they attribute meaning to
'objective probabilities' (for instance, cases of symmetry as for dice etc.,
'statistical' cases of 'repeatable' events, etc.)."
"Prevision […] does not involve guessing anything. It does not assert - as prediction does - something that might turn out to be true or false, by transforming (over-optimistically) the uncertainty into a claimed, but worthless, certainty. It acknowledges (as should be obvious) that what is uncertain is uncertain: in so far as statements are concerned, all that can be said beyond what is said by the logic of certainty is illegitimate." (Bruno de Finetti, "Theory of Probability", 1974)
"Probability does not exist; it is a subjective description of a person’s uncertainty. We should be normative about uncertainty and not descriptive." (Bruno de Finetti, "Theory of Probability", 1974)
"Probability, too, if regarded as something endowed with some
kind of objective existence, is no less a misleading misconception, an illusory
attempt to exteriorize or materialize our true probabilistic beliefs." (Bruno de
Finetti, "Theory of Probability", 1974)
"Specifically, it seems to me preferable to use, systematically: 'random' for that which is the object of the theory of probability […]; I will therefore say random process, not stochastic process. 'stochastic' for that which is valid 'in the sense of the calculus of probability': for instance; stochastic independence, stochastic convergence, stochastic integral; more generally, stochastic property, stochastic models, stochastic interpretation, stochastic laws; or also, stochastic matrix, stochastic distribution, etc. As for 'chance', it is perhaps better to reserve it for less technical use: in the familiar sense of'by chance', 'not for a known or imaginable reason', or (but in this case we should give notice of the fact) in the sense of, 'with equal probability' as in 'chance drawings from an urn', 'chance subdivision', and similar examples." (Bruno de Finetti, "Theory of Probability", 1974)
"The calculus of probability can say absolutely nothing about reality [...] We have to stress this point because these attempts assume many forms and are always dangerous. In one sentence: to make a mistake of this kind leaves one inevitably faced with all sorts of fallacious arguments and contradictions whenever an attempt is made to state, on the basis of probabilistic considerations, that something must occur, or that its occurrence confirms or disproves some probabilistic assumptions." (Bruno de Finetti, "Theory of Probability", 1974)
"The logic of certainty furnishes us with the range of possibility (and the possible has no gradations); probability is an additional notion that one applies within the range of possibility, thus giving rise to graduations (‘more or less’ probable) that are meaningless in the logic of uncertainty." (Bruno de Finetti, "Theory of Probability", 1974)
"The field of probability and statistics is then transformed into a Tower of Babel, in which only the most naive amateur claims to understand what he says and hears, and this because, in a language devoid of convention, the fundamental distinctions between what is certain and what is not, and between what is impossible and what is not, are abolished. Certainty and impossibility then become confused with high or low degrees of a subjective probability, which is itself denied precisely by this falsification of the language. On the contrary, the preservation of a clear, terse distinction between certainty and uncertainty, impossibility and possibility, is the unique and essential precondition for making meaningful statements (which could be either right or wrong), whereas the alternative transforms every sentence into a nonsense." (Bruno de Finetti, "Theory of Probability", 1974)
"To make a prediction would mean (using the term in the sense we propose) to venture to try to 'guess', among the possible alternatives, the one that will occur. This is an attempt often made, not only by would-be magicians and prophets, but also by experts and such like who are inclined to precast the future in the forge of their fantasies). To make a 'prediction', therefore, would not entail leaving the domain of the logic of certainty, but simply including the statements and data which we assume ourselves capable of guessing, along with the ascertained truths and the collected data." (Bruno de Finetti, "Theory of Probability", 1974)
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